Respuesta :
Probability first is a woman: P( 1W)
[tex]\begin{gathered} P(1W)=\frac{\#\text{women}}{\#persons\text{ line up}} \\ \\ P(1W)=\frac{3}{6}=\frac{1}{2}=0.5 \end{gathered}[/tex]The probability that the first person in the line is a woman is 1/2 or 0.5 or 50%.
To find the probability of the alternate by gender:
Find the probability that the second person is a man P(2M). Knowing that the first person is a woman.
In this case the number of persons line up is 5 (as you don't need to count the first person):
[tex]\begin{gathered} P(2M)=\frac{\#\text{men}}{\#persons\text{ line up left}} \\ \\ P(2M)=\frac{3}{5}=0.6 \end{gathered}[/tex]find the probability that the third person is a woman P(3W):
[tex]\begin{gathered} P(3W)=\frac{\#\text{women left}}{\#persons\text{ line up left }} \\ \\ P(3W)=\frac{2}{4}=\frac{1}{2}=0.5 \end{gathered}[/tex]Find the probability that the fourth person is a man:
[tex]\begin{gathered} P(4M)=\frac{\#\text{men left}}{\#persons\text{ line up left}} \\ \\ P(4M)=\frac{2}{3}=0.6\bar{6} \end{gathered}[/tex]find the probability that the fifth person is a woman:
[tex]\begin{gathered} P(5W)=\frac{\#\text{women left}}{\#persons\text{ line up left}} \\ \\ P(5W)=\frac{1}{2}=0.5 \end{gathered}[/tex]Find the probability that the sixth person is a man:
[tex]\begin{gathered} P(6M)=\frac{\#\text{man left}}{\#persons\text{ line up left}} \\ \\ P(6M)=\frac{1}{1}=1 \end{gathered}[/tex]Then, multiply all six probabilities:
[tex]\frac{1}{2}\cdot\frac{3}{5}\cdot\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{1}{2}\cdot1=\frac{6}{120}=\frac{1}{20}=0.05[/tex]Then, the probbility taht the first person is a woman and then alternate by gender is 1/20 or 0.05 or 5%
